Fabrication of diffraction gratings

ABSTRACT

The systems and methods discussed herein are for the fabrication of diffraction gratings, such as those gratings used in waveguide combiners. The waveguide combiners discussed herein are fabricated using nanoimprint lithography (NIL) of high-index and low-index materials in combination with and directional etching high-index and low-index materials. The waveguide combiners can be additionally or alternatively formed by the directional etching of transparent substrates. The waveguide combiners that include diffraction gratings discussed herein can be formed directly on permanent transparent substrates. In other examples, the diffraction gratings can be formed on temporary substrates and transferred to a permanent, transparent substrate.

PRIORITY CLAIM

This application claims priority to U.S. Provisional App. No.62/691,421, “Fabrication of Diffraction Gratings,” filed Jun. 28, 2018,incorporated herein in its entirety by reference, and U.S. ProvisionalApp. No. 62/692,286, “Fabrication of Diffraction Gratings,” filed Jun.29, 2018, incorporated herein in its entirety by reference.

BACKGROUND Field

The embodiments of the disclosure generally relate to optical elementstructures and systems and methods of fabricating optical elementstructures such as those used in various types of waveguides.

Description of the Related Art

Waveguides are structures that guide electromagnetic or sound waves byenabling a signal to propagate with a minimal loss of energy byrestricting the expansion of the signal one dimension or two dimensions.Waves propagate in three dimensions, and the wave can lose power as itpropagates away from the source that generated the wave, such as a soundwave or an electromagnetic wave. By confining the waves such that theypropagate in one or two dimensions, the power of the wave is conserved.The waveguide thus preserves the power of the wave while it propagates.

Waveguide combiners are used to combine signals such as RF signals byaccepting multiple input signals and producing a single output signalthat is a combination of the input signals. As demand for waveguidesincreases, for example, in optical fiber applications, radarapplications, scientific instrumentation, and augmented reality, ademand for waveguides increases, and current technologies involve makingmaster patterns and doing imprint replication to form a grating, so onlymaterials that are imprint-able can be used for waveguide fabrication.

Thus, there remains a need for systems and methods of improved waveguidemanufacturing.

SUMMARY

Systems and methods discussed herein are directed towards methods offorming gratings. In one example, a method of pattering a substrateincludes forming a hardmask layer on a first side of a substrate,wherein the substrate is formed from a transparent material and isdefined by a normal plane along a width of the substrate; and forming,by nanoimprint lithography, on the hardmask layer, a patterned layer. Inthe example, the method further includes etching the patterned layer andthe hardmask layer to expose the first side of the substrate; removingthe patterned layer; and etching the first side of the substrate to forma first plurality of angled mesas in the first side of the substrate.Each angled mesa of the first plurality of angled mesas is etched at anangle from 20 degrees to 70 degrees relative to the normal plane.Further in the method, subsequent to etching the first side of thesubstrate, removing the hardmask layer.

In another examples, a method of forming a grating includes: forming ahardmask layer on a target stack, wherein the target stack is formed ona first side of a first substrate; etching a plurality of openings inthe hardmask layer; and etching the target stack to form a firstplurality of angled mesas in the target stack on the first side of thefirst substrate. Each angled mesa of the first plurality of angled mesasis etched at a first angle from 20 degrees to 70 degrees relative to anormal plane.

In another example, a method of forming a grating includes: forming ahardmask layer on a target stack, wherein the target stack is formed ona first side of a first substrate; etching a plurality of openings inthe hardmask layer; and etching the target stack to form a firstplurality of angled mesas in the target stack on the first side of thefirst substrate. Each angled mesa of the plurality of angled mesas isetched at an angle 20 degrees to 70 degrees relative to a normal plane.The method further includes forming a hardmask layer on a second side ofthe first substrate, wherein the first substrate is defined by a normalplane along a width of the substrate; and forming, by nanoimprintlithography, a patterned layer on the hardmask layer.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentdisclosure can be understood in detail, a more particular description ofthe disclosure, briefly summarized above, may be had by reference toembodiments, some of which are illustrated in the appended drawings. Itis to be noted, however, that the appended drawings illustrate onlyexemplary embodiments and are therefore not to be considered limiting ofits scope, and may admit to other equally effective embodiments.

FIG. 1 is a flow chart of a method of forming a grating structuredirectly on a transparent substrate according to embodiments of thepresent disclosure.

FIGS. 2A-2F are partial schematic illustrations of operations of theformation of a grating structure according to embodiments of the presentdisclosure.

FIG. 3 is a flow chart of a method of forming a grating structuredirectly on a transparent substrate according to embodiments of thepresent disclosure.

FIGS. 4A-4E are partial schematic illustrations of the formation of agrating structure according to embodiments of the present disclosure.

FIG. 5 is a method of transferring a grating structure from a firstsubstrate to a second substrate according to embodiments of the presentdisclosure.

FIGS. 6A-6E are partial schematic illustrations of the formation of agrating structure according to embodiments of the present disclosure.

FIG. 7 is a method of transferring a grating structure from a firstsubstrate to a second substrate according to embodiments of the presentdisclosure.

FIGS. 8A-8E are partial schematic illustrations of the formation of agrating structure according to embodiments of the present disclosure.

FIG. 9 is a method of directly etching a grating structure in atransparent substrate according to embodiments of the presentdisclosure.

FIGS. 10A-10F are partial schematic illustrations of the formation of agrating structure according to embodiments of the present disclosure.

FIGS. 11A-11C are flow charts of methods used to fabricate a waveguidecombiner according to embodiments of the present disclosure.

FIG. 12 is a partial schematic illustration of a waveguide combinerstructure fabricated according to embodiments of the present disclosure.

To facilitate understanding, identical reference numerals have beenused, where possible, to designate identical elements that are common tothe figures. It is contemplated that elements and features of oneembodiment may be beneficially incorporated in other embodiments withoutfurther recitation.

DETAILED DESCRIPTION

The systems and methods discussed herein can include the mass productionof diffraction gratings used for waveguides. Augmented reality surfacerelief waveguide combiners are made by a process of mastering andreplication. Currently, these waveguide combiners have only beenproduced in quantities of thousands, whereas future projected volumesare in the tens of millions or greater. Challenges in the currentmanufacturing process include the reproducibility of the shapesreplicated, especially as in high volume production, include concernsregarding the yield in the nanoimprint lithography (NIL) process.Further challenges include the release after the NIL imprinting of highangle gratings since the gratings can be formed at an angle of 45degrees or greater with respect to the normal plane.

As discussed herein, materials with a low refractive index, “low-index”materials, can include silicon dioxide (SiO₂), doped SiO₂, fluorinatedpolymers, or porous materials. Materials with a high refractive index,“high-index” materials, can include amorphous and crystalline Si,silicon nitride (SiN), titanium dioxide (TiO₂), gallium phosphate (GaP),tantalum pentoxide (Ta₂O₅), or sulfur-inated materials and polymers.

Discussed herein are systems and methods for fabricating waveguidedevices using direct etching and NIL. Waveguide devices includingwaveguide combiners include a plurality of diffraction gratings formedin a low-index material, a high-index material, or a combination of lowand high-index materials, and a plurality of gratings formed in anoptically transparent substrate such as polymer or glass. As discussedherein, a “transparent” substrate is a substrate that is opticallytransparent in a predetermined wavelength range within which thewaveguide combiner is intended to operate. As discussed herein, adiffraction grating can be referred to as a “grating” or “gratings” andcan include a plurality of angled mesas, which can also be referred toas teeth or fins, and a plurality of troughs formed in between adjacentangled mesas. In some examples, the troughs of a grating do not containfill material, and in other examples, the troughs of a grating arefilled with various materials. In one example, the mesas of a gratingcan be formed from a low-index material, and the troughs of the gratingare filled with a high-index material. In another example, the angledmesas of a grating can be formed from a high-index material, and thetroughs of the grating are filled with a low-index material. The angledmesas and troughs within a grating can be uniform in one or more ofwidth, length, spacing, or angle with respect to a normal plane of thesubstrate. In another example, the angled mesas and troughs of a gratingcan differ in one or more of width, length, spacing, or angle withrespect to a normal plane of the substrate.

As discussed in various embodiments herein, NIL can be used along withdirect etching to fabricate a waveguide combiner. In some examples, adouble-sided processing method is used to fabricate a waveguidecombiner. The double-sided fabrication method includes forming a firstgrating in a target stack formed of at least one of a low or ahigh-index material by using NIL on a transparent substrate, and forminga second grating using direct etching on the other side of the samesubstrate. One of the challenges in a direct etch is performinglithography on glass substrates. For example, a conventional lithographyprocess can be configured to accept a substrate with a maximum thicknessof 775 μm due to lithography scanner parameters. Waveguide combiners arecurrently made using a glass substrate, with a thickness depending onthe design, but are typically 0.5 mm or 0.8 mm thick, which issignificantly thinner than what the lithography scanner is configured toprocess.

In one embodiment, a grating is formed using NIL and direct etching on atemporary substrate that can be formed from silicon. The grating is thende-bonded from the temporary substrate and transferred to a second,transparent substrate that can include glass. In another embodiment, thegrating is formed via NIL and direct etching on a target layer alreadydisposed on a glass or other transparent substrate. A grating can alsobe formed using NIL and direct etching in the transparent substrate.High angle gratings are formed using the systems and methods discussedherein, the angles may range from 20 degrees to 70 degrees from a normalplane parallel to the substrate. The waveguides and waveguide componentsdiscussed herein are formed by direct etching of the devices, and can befabricated using temporary or permanent binding, in combination withNIL.

In other examples, waveguide designs with a wide range of duty cycles(DC) (i.e. the radio of the mesa width to the mesa pitch) are desirable.It can be challenging to fabricate this range of duty cycles with NILdue to imprint material shrinkage. However, in some embodiments, thischallenge is overcome by imprinting a low index & low duty cyclegrating, then filling the low duty cycle grating with a high indexmaterial to form a grating with a high duty cycle and a high indexgrating.

FIG. 1 is a flow chart of a method 100 of forming a grating structuredirectly on a transparent substrate. FIGS. 2A-2F are partial schematicillustrations of operations of the method 100. FIGS. 1 and 2A-2F arereferenced together below.

At operation 102 of the method 100, and as shown in a structure 200A inFIG. 2A, a target stack 204 is formed on a substrate 202. The substrate202 can be formed from a transparent substrate such as a glass or apolymer substrate which can be from 0.5 mm to 0.8 mm. At operation 104,a hardmask layer 206 is formed over the target stack 204 as shown inFIG. 2A. The target stack 204 can be fabricated of SiN, TiO₂, GaP, oranother high-index material, and is deposited by CVD, PVD, spinning-on,or another appropriate method at operation 102. In one embodiment, athickness of the target stack 204 can be from 100 nm to 500 nm,depending on the index and optical wavelength to be used in the finishedwaveguide combiner device. The hardmask layer 206 can be fabricated fromTiN, TaN, Cr, or another etch-resistant material deposited by CVD, PVD,ALD or another thin-film deposition process at operation 104. Thehardmask layer 206 can be formed at operation 104 to a thickness fromabout 10 nm to about 50 nm. In some examples, a hardmask layer 206 ofless than 25 nm thick can be employed to reduce or avoid shadowingduring subsequent etching operations.

At operation 106 of the method 100, and as shown in a structure 200B inFIG. 2B, a pattern layer 208 is formed on the hardmask layer 206 usingNIL. The pattern layer 208 is formed of an imprintable resist material.The pattern layer is formed of a plurality of raised features 210, Aplurality of gaps 212 are formed between adjacent pairs of raisedfeatures 210. Each gap of the plurality of gaps 212 has a bottomresidual layer 214 of the pattern layer 208. In an embodiment atoperation 106, the NIL of the hardmask is performed with an angle δbetween each of the raised features 210 and the substrate 202. The angleδ can be greater than 90 degrees, which can decrease cost and promotethe formation of subsequent features during directional etching asdiscussed herein.

Subsequently, at operation 108, and as shown in a structure 200C in FIG.2C, a portion of the hardmask layer 206 and the pattern layer 208 isremoved via etching. As such, a bottom 216 of each gap 212 exposes thetarget stack 204 and a plurality of hardmask mesas 218 is formed. Atoperation 110 of the method 100, as shown in a structure 200D in FIG.2D, the pattern layer 208 is removed, exposing the plurality of hardmaskmesas 218. At operation 112, as shown in a structure 200E in FIG. 2E,the target stack 204 is etched to form a plurality of angled mesas 222and a plurality of troughs 220 in between the angled mesas 222, theetching at operation 112 exposes the substrate 202. The plurality ofangled mesas 222 can be formed at an angle α from the normal plane 224of the substrate 202. The etching at operation 112 can be referred to asdirectional etching. The angle α can be from 20 degrees to 70 degrees.

At operation 114, as shown in a structure 200F in FIG. 2F, the remainingportion of the hardmask layer 206 is removed, leaving the plurality ofangled mesas 222 and the plurality of troughs 220 formed to a depth of226. The directional etching discussed herein is performed, in oneexample, by positioning a first portion of the substrate 202 that isretained on a platen in a first position in a path of an ion beam in anetching chamber. The ion beam can be a ribbon beam, a spot beam, or afull, substrate-size beam that extends across a substrate from a firstedge to a second edge that is parallel to the first edge. The ion beamis configured to contact a top surface of a target material, such as thetarget stack 204, to form a first grating that includes the angled mesas222. The ion beam angle can be from 0 to 90 (i.e. any angle desired),but the ion beam is typically set at the desired etch angle (e.g. 20 to70 degrees) relative to the normal plane of the substrate 202, such thatthe ion beam attacks the target stack 204 at the maximum angle desired.To obtain etches with lower angles than the maximum angle set by the ionbeam direction the substrate 202 retained on the platen can be rotatedabout an axis of the platen to a predetermined rotation angle. Therotation results in the ion beam contacting the top surface of thetarget stack 204 at a different angle to form a second or othersubsequent gratings. The amount of substrate rotation, e.g., thepredetermined rotation angle used can be calculated to produce the exactgrating etch angle desired.

In an alternate embodiment, the directional etching at operation 112 canbe controlled (e.g., control of the etch depth, etch angle, and etchrate) by adjusting a hardmask thickness across the various gratingsdiscussed herein. The hardmask thickness adjustment can be achieved byetching of the hardmask and/or by NIL, in some examples, NIL can be morecost-effective. In this example, when the directional etching atoperation 112 is performed, the final depth of the plurality of troughs220, as shown by 226 in FIG. 2F, can vary depending on the thickness ofthe hardmask layer 206 (formed by NIL at operation 106) at differentlocations on the grating.

FIG. 3 is a flow chart of a method 300 of forming a grating structuredirectly on a transparent substrate. FIGS. 4A-4E are partial schematicillustrations of the method 300. FIGS. 3 and 4A-4E are discussedtogether below.

At operation 302 of the method 300, a target stack 404 is formed on asubstrate 402, as shown in structure 400A in FIG. 4A. The substrate 402is transparent and can be formed from a polymer, glass, ceramic, orother optically transparent materials. The target stack 404 is formedvia chemical vapor deposition (CVD) to a thickness from 100 nm to 500nm. In alternate embodiments, PVD, spinning-on, or ALD can be used toform the target stack 404. At operation 304, a hardmask 406 is formedvia NIL on the target stack 404, as shown in structure 400B in FIG. 4B.The hardmask 406 is formed as a layer of features 408 and gaps 410 inbetween adjacent features 408. A bottom 412 of each gap 410 has thehardmask 406 formed thereon. The hardmask 406 can be fabricated from ametal or metal oxide or metal nitride, including TiN or TaN, or carbon,or from another etch-resistant nano-imprintable material. At operation306, as shown in structure 400C in FIG. 4C, the bottom 412 layer ofhardmask 406 in each gap 410 is removed via etching to expose the targetstack 404. At operation 308, shown in structure 400D in FIG. 4D thetarget stack 404 is etched to form a plurality of angled mesas 414. Theplurality of angled mesas 414 can be formed at an angle α from thenormal plane 418 of the substrate 402. The angle α can be from 20degrees to 70 degrees. While each of the plurality of angled mesas 414is shown in FIG. 4D with a similar width 420, in other examples, thewidths or other dimensions among and between the angled mesas 414,including the angle α, can vary. The angled mesas 414 can be formed bydirectionally etching using tooling configured to direct etchants at anangle relative to the target stack 404. At operation 310, the hardmask406 is removed, as shown in structure 400E in FIG. 4E. The method 300can be used when it may be desirable to form the hardmask 406 inoperation 304, in contrast to methods discussed herein where a hardmaskis deposited in a first operation and then patterned in a secondoperation.

FIG. 5 is a method 500 of transferring a grating structure from a firstsubstrate to a second substrate according to embodiments of the presentdisclosure. FIGS. 6A-6E are partial schematic illustrations of themethod 500. FIGS. 5 and 6A-6E are discussed together below.

FIG. 6A illustrates a structure fabricated similarly to the structuresfabricated according to the methods 100 and 300 in FIGS. 1 and 3discussed above. However, instead of being formed on a transparentsubstrate as discussed above, FIG. 6A shows a structure 600A including agrating 606 formed on a first substrate 602 comprising silicon. Ade-bonding layer 604 is formed by growing a thin layer of silicondioxide with CVD, or spinning on a thin adhesive in between the firstsubstrate 602 and the grating 606. The grating 606 includes a pluralityof angled mesas 608 and a plurality of troughs 610 in between each pairof adjacent angled mesas 608. The first substrate 602 can be formed fromsilicon. In another example, which can be combined with other examplesherein, the grating 606 can be formed from a high-index material, andthe de-bonding layer 604 can be formed from a thermally-responsiveadhesive or layer of SiO₂. At operation 502 of the method 500, thestructure of FIG. 6A is received in a process chamber. At operation 504,a fill layer 612 is deposited in the troughs 610 and over the angledmesas 608 of the grating 606, as shown in structure 600B FIG. 6B. Insome examples, during operation 504, the fill layer 612 forms a layer614 on top of the angled mesas 608. This layer 614 of low-index materialis removed at operation 506, as shown in structure 600C in FIG. 6C, viamechanical means, chemical means, or a combination of thereof. Atoperation 508, shown in structure 600D in FIG. 6D, the structure 600D isbonded to a glass substrate 618 on a side opposite of where the firstsubstrate 602 was bonded. At operation 510, shown in structure 600E inFIG. 6E, the first substrate 602 is removed via thermal means, such thatthe de-bonding layer 604 releases from the grating 606, or by grindingan polishing away the silicon wafer to stop on the SiO₂.

FIG. 7 is a method 700 of transferring a grating structure from a firstsubstrate to a second substrate according to embodiments of the presentdisclosure. FIGS. 8A-8E are partial schematic illustrations of themethod 700. FIGS. 7 and 8A-8E are referenced together below.

FIG. 8A illustrates a structure 800A fabricated similarly to thestructures fabricated according to the methods 100 and 300 in FIGS. 1and 3 discussed above. However, instead of being formed on a transparentsubstrate as discussed above, FIG. 8A shows a grating 806 formed on afirst substrate 802. In one example, the first substrate 802 is formedfrom silicon. A de-bonding layer 804 is formed in between the firstsubstrate 802 and the grating 806. The grating 806 comprises a pluralityof angled mesas 808 and a plurality of troughs 810 in between the angledmesas 808. In one example, the first substrate 802 can be formed fromsilicon. In another example, that can be combined with other examplesherein, the grating 806 can be formed from a low-index material. Thede-bonding layer 804 can be formed from a thermally-responsive adhesive.At operation 702 of the method 700, the structure of FIG. 8A is receivedin a process chamber. At operation 704, a fill layer 812 is deposited inthe troughs 810 and over the angled mesas 608 of the grating 806, asshown in structure 800B in FIG. 8B. In some examples, during operation704, the fill layer 812 includes a layer 814 on top of the angled mesas808. This layer 814 of high-index material is removed at operation 706,as shown in structure 800C in FIG. 8C, via mechanical means, chemicalmeans, or a combination of thereof. At operation 708, shown in structure800D in FIG. 8D, the first substrate 802 is removed via thermal means,such that the de-bonding layer 804 releases from the grating 806. Atoperation 710, shown in structure 800E in FIG. 8E, the structure 800D ofFIG. 8D is bonded to a glass substrate 818 on a side opposite of wherethe first substrate 802 was bonded.

FIG. 9 is a method 900 of directly etching a grating structure in atransparent substrate. FIGS. 10A-10F are partial schematic illustrationsof the method 900. FIGS. 9 and 10A-10F are referenced together below.

In method 900, at operation 902, as shown in structure 1000A in FIG.10A, a hardmask 1004 is formed on a transparent substrate 1002. Thetransparent substrate 1002 can be formed from glass, polymer, or othermaterials that are optically transparent. The hardmask 1004 can beformed of TiN, TaN, Cr, or other etch resistant materials, and is formedat operation 902 via CVD, PVD, ALD, or other methods to a thickness from10 nm to 50 nm. At operation 904, as shown in structure 1000B in FIG.10B, a pattern is formed by NIL to create layer 1006. The layer 1006 isformed as a plurality of mesas 1010 and troughs 1012. A bottom 1008 ofeach trough 1012 is formed from a residual layer of the material of thelayer 1006. The layer 1006 can be a low-index material or a high-indexmaterial, depending upon the embodiment. The layer 1006 is etched, alongwith the hardmask 1004, at operation 906 to form structure 1000C shownin FIG. 100. Etching the layer 1006 and the hardmask 1004 at operation906 exposes the transparent substrate 1002 at the bottom 1014 of thetroughs 1012. At operation 908, shown in structure 1000D in FIG. 10D,the layer 1006 is removed, leaving a plurality of hardmask islands 1016.At operation 910, shown in structure 1000E in FIG. 10E, the transparentsubstrate 1002 is etched to form a plurality of angled mesas 1022 with aplurality of troughs 1018 formed in between each adjacent pair of angledmesas 1022. Each angled mesa 1022 of the plurality of angled mesas 1022is at an angle α from a normal plane 1024. A bottom 1020 of each trough1018 is the substrate material. At operation 912, shown in FIG. 10F, thehardmask 1004 is removed, removing the hardmask islands 1016, leavingbehind the structure 1000F of the transparent substrate 1002.

FIGS. 11A-11C are flow charts of methods used to fabricate a waveguidecombiner according to embodiments of the present disclosure.

FIG. 11A shows a method 1100A of forming a diffraction grating, whichcan be used in a waveguide combiner, according to embodiments of thepresent disclosure. At operation 1102, a patterned target layer isformed on a de-bonding layer attached to a first substrate that can beformed from silicon (Si). The operation 1102 can include some or theelements of the methods 500 or 700 in FIG. 5 or 7, respectively, each ofwhich forms a pattern on a Si substrate, de-bonds the substrate, andattaches a transparent substrate of glass, plastic, or another opticallytransparent material. The operation 1102 includes the transferring ofthe patterned target layer, which can be formed from a combination of ahigh index layer and a low index layer, depending upon the embodiment.In one example, the operation 1102 includes transferring the patternedtarget layer to a first side of a transparent substrate. At operation1104, a second side of the transparent substrate is patterned, forexample, according to the method 900 in FIG. 9, to form the waveguidecombiner at operation 1106.

FIG. 11B shows a method 1100B of forming one or more diffractiongratings, which can be used in a waveguide combiner, according toembodiments of the present disclosure. At operation 1108, a patternedtarget layer is formed a transparent substrate, similar to what isdescribed in the methods 100 and 300 in FIGS. 1 and 3. At operation1110, the second side of the transparent substrate is patterned, forexample, according to the method 900 in FIG. 9, to form the waveguidecombiner at operation 1112.

FIG. 11C shows a method 1100C of forming one or more diffractiongratings, which can be used in a waveguide combiner, according toembodiments of the present disclosure. At operation 1114, a patternedlayer is formed in a first side of a transparent substrate that can beformed from glass or polymer, operation 1114 can be executed accordingto the method 900 in FIG. 9. At operation 1116, a patterned target layeris formed on a second side of the transparent substrate according to amethod 100 or 300 as shown in FIGS. 1 and 3 to form the waveguidecombiner at operation 1118.

FIG. 12 is a partial schematic illustration of a waveguide combinerstructure 1200 fabricated through the methods of FIGS. 11A-11C. FIG. 12shows the waveguide combiner structure 1200 comprising a transparentsubstrate 1202, and a first grate structure 1204 formed according toembodiments of the present disclosure, including the methods 100, 300,500, and 700 in FIGS. 1, 3, 5, and 7, respectively. The first gratestructure 1204 is shown in the example in FIG. 12 as comprising theangled mesas 1208, each of which are formed at an angle of a withrespect to a normal plane 1228. The angle α can be from 20 degrees to 70degrees. Each angled mesa 1208 can be formed from low-index material orhigh-index material, depending upon the embodiment. While a plurality oftroughs 1210 are shown in FIG. 12 in between each pair of adjacentangled mesas 1208 as not comprising a material, in alternateembodiments, the troughs 1210 are filled with a low-index or ahigh-index material. If the angled mesas 1208 are formed from alow-index material, the troughs 1210 can be filled with a high-indexmaterial, and, if the angled mesas 1208 are formed from a high-indexmaterial, the troughs 1210 can be filled with a low-index material. Eachangled mesa 1208 has a width 1212, a length 1214, and a spacing 1216between adjacent angled mesas 1218. Each of the width 1212, the length1214, and the spacing 1216 is shown in the example waveguide combinerstructure 1200 as being substantially the same, as are the angles α.However, in other examples, one or more of these dimensions may varyamong and between individual angled mesas 1208 or among and betweengroups, such as rows, columns, or combinations thereof.

The waveguide combiner structure 1200 further includes a second gatestructure 1206 comprising a plurality of angled mesas 1218, formed inthe transparent substrate 1202. A plurality of troughs 1220 are formedin between each adjacent pair of angled mesas 1218, and the angled mesas1218 are formed at an angle of β with respect to the normal plane 1228.The angle β can be less than or equal to about 45 degrees. Each angledmesa 1218 is formed a distance from 1222 from an adjacent angled mesa1218, and has a width 1226 and a length 1224. The distances 1222 inbetween angled mesas 1218 as well as the width 1226 and the length 1224are shown as being substantially the same among and between angled mesas1218. However, in alternate embodiments, one or more of these dimensionsmay vary among and between individual angled mesas 1218 or among andbetween groups, such as rows, columns, or combinations thereof.

Accordingly, using the systems and methods for waveguides and waveguidecombiners discussed herein, waveguides and waveguide combiners that havea wide range of duty cycles (DC) (i.e. the radio of the mesa width tothe mesa pitch) are fabricated. In one example, the challenge ofshrinkage of the imprinted materials is overcome by imprinting a lowindex & low duty cycle grating. The imprinted structures are then filledwith a high index material to form a grating with a high duty cycle anda high index grating. The examples of diffracting grating formationdiscussed herein can be combined with other examples herein to formdiffraction gratings included in waveguides and waveguide combiners.

Although various embodiments which incorporate the teachings of thepresent invention have been shown and described in detail herein, thoseskilled in the art can readily devise many other varied embodiments thatstill incorporate these teachings.

What is claimed is:
 1. A method of pattering a substrate, comprising:forming a hardmask layer on a first side of a substrate, wherein thesubstrate is formed from a transparent material and is defined by anormal plane along a width of the substrate; forming, by nanoimprintlithography, on the hardmask layer, a patterned layer; etching thepatterned layer and the hardmask layer to expose the first side of thesubstrate; removing the patterned layer; etching the first side of thesubstrate to form a first plurality of angled mesas in the first side ofthe substrate, wherein each angled mesa of the first plurality of angledmesas is etched at an angle from 20 degrees to 70 degrees relative tothe normal plane; and subsequently, removing the hardmask layer.
 2. Themethod of claim 1, wherein forming the hardmask layer on the first sideof the substrate comprises using chemical vapor deposition (CVD),physical vapor deposition (PVD), or atomic layer deposition (ALD). 3.The method of claim 1, wherein the transparent material comprises aglass or a polymer.
 4. The method of claim 1, further comprising:forming a pattern on a second side of the substrate, the pattern on thesecond side of the substrate comprising a second plurality of angledmesas, the second plurality of angled mesas being at a different anglethan the first plurality of angled mesas.
 5. The method of claim 4,wherein nanoimprint lithography is used in the forming of the secondplurality of angled mesas on the second side of the substrate.
 6. Amethod of forming a diffraction grating, comprising: forming a hardmasklayer on a target stack, wherein the target stack is formed on a firstside of a first substrate; etching a plurality of openings in thehardmask layer; and etching the target stack to form a first pluralityof angled mesas in the target stack on the first side of the firstsubstrate, wherein each angled mesa of the first plurality of angledmesas is etched at a first angle from 20 degrees to 70 degrees relativeto a normal plane.
 7. The method of claim 6, wherein forming thehardmask layer comprises using nanoimprint lithography (NIL) to depositthe hardmask layer as a pattern, wherein the pattern comprises a thirdplurality of mesas and a plurality of angled troughs in between adjacentmesas of the third plurality of mesas.
 8. The method of claim 6, furthercomprising: forming a hardmask layer on a second side of the firstsubstrate, wherein the first substrate comprises a transparent materialand is defined by a normal plane along a width of the first substrate;forming, by nanoimprint lithography, a patterned layer on the hardmasklayer; etching the patterned layer and the hardmask layer to expose thesecond side of the first substrate; removing the patterned layer;etching the second side of the first substrate; forming, in response tothe etching, a second plurality of angled mesas in the second side ofthe first substrate, wherein each angled mesa of the second plurality ofangled mesas is etched at a second angle from 20 degrees to 70 degreesrelative to the normal plane.
 9. The method of claim 6, furthercomprising attaching a transparent substrate to the target stack. 10.The method of claim 8, further comprising removing the first substratesubsequent to forming the first plurality of angled mesas in the targetstack, wherein the target stack is bonded to the first substrate via ade-bonding layer, wherein removing the first substrate comprisesdetaching the first substrate from the target stack via the de-bondinglayer.
 11. The method of claim 8, wherein forming the hardmask layer onthe second side of the first substrate comprises using nanoimprintlithography (NIL) to deposit the hardmask layer as a pattern, whereinthe pattern comprises a plurality of mesas and a plurality of angledtroughs in between the mesas.
 12. The method of claim 8, furthercomprising etching each of the target stack and the second side of thefirst substrate using directional etching.
 13. The method of claim 12,wherein directional etching comprises: positioning a first portion ofthe target stack in a path of an ion beam, the ion beam being at thefirst angle relative to the normal plane of the first substrate, whereinetching the first portion of the target stack comprises exposing thefirst portion of the target stack to the ion beam to form the firstplurality of angled mesas at the first angle; and rotating the firstsubstrate about a central axis perpendicular to the normal plane to apredetermined rotation angle.
 14. The method of claim 13, furthercomprising positioning a second portion of the target stack in the pathof the ion beam after rotating the first substrate to the predeterminedrotation angle; and etching the second portion of the target stack toform a third plurality of mesas by exposing the second portion of thetarget stack to the ion beam.
 15. A method of forming diffractiongratings, comprising: forming a hardmask layer on a target stack,wherein the target stack is formed on a first side of a first substrate;etching a plurality of openings in the hardmask layer; etching thetarget stack to form a first plurality of angled mesas in the targetstack on the first side of the first substrate, wherein each angled mesaof the plurality of angled mesas is etched at an angle 20 degrees to 70degrees relative to a normal plane; forming a hardmask layer on a secondside of the first substrate, wherein the first substrate is defined by anormal plane along a width of the first substrate; and forming, bynanoimprint lithography, a patterned layer on the hardmask layer. 16.The method of claim 15, further comprising: etching the patterned layerand the hardmask layer to expose the second side of the first substrate;removing the patterned layer; and etching the second side of the firstsubstrate.
 17. The method of claim 16, further comprising: forming, inresponse to the etching, a plurality of angled mesas in the second sideof the first substrate, wherein each angled mesa of the plurality ofangled mesas is etched at an angle from 20 degrees to 70 degreesrelative to the normal plane.
 18. The method of claim 15, whereinforming the hardmask layer comprises using nanoimprint lithography (NIL)to deposit the hardmask layer as a pattern, wherein the patterncomprises a plurality of mesas and a plurality of angled troughs inbetween the mesas.
 19. The method of claim 15, wherein forming thehardmask layer on the first substrate comprises using chemical vapordeposition (CVD), physical vapor deposition (PVD), or atomic layerdeposition (ALD).
 20. The method of claim 15, wherein the firstsubstrate is optically transparent and comprises a glass or a polymer.